When you had the platform constructed did you include a method for keeping it attached to the forklift? Such as bolts at the back of the "hollow beams" that would fit behind the forks or anchor points for chains that woud go behind the mast assembly?

The guidelines for using such a platform in the UK are:
A. It must be secured to the forks or carriage so that it cannot come off
B. The platform must meet the construction and inspection requirements set out
by the HSE
C. There must be a safe method of use agreed before starting the work
D. Only authorised persons operate and are lift ed in the manned platform
E. The operator must not leave the lift truck whilst the occupants are in the cage
F. Only the lift and lower lever shall be used
G. No other hydraulic levers should be used
H. The lift truck must be on level ground
I. The operation must be for occasional non-scheduled use
J. A thorough risk assessment of the lift must be in place
K. The lift truck must be secured by use of the handbrake and neutral applied
L. The thorough examination frequency of the lift truck must be at least 6 monthly
M. Persons are not to be transported within the cage
N. A method of communication is agreed between the operator and person(s) lift ed
prior to the work commencing

I have seen people using ratchet straps to hold it against the mast assembly frame or the backrest extension, but tghink that woud lbe a short term fix.
I woudl suggest you look at the entry point for the forks and see if it is possible to drill a hole towards the rear so that you can fit retaining bolts or similar that fit behind the forks to keep the platform in position because using the fork spacing is not a solution.